Modern society relies on measurements: trade and commerce are based on legal systems of 'weights and measures' and measurements are made incessantly, for our comfort, safety and well-being.
Yet measurement can only estimate the value intended to be measured: there will always be a difference between the result obtained and the actual, unknown, value.
This simply cannot be avoided. So, to be confident that a measurement is 'fit for purpose', the measurement uncertainty – the uncertainty of a result as an estimate of quantity intended to be measured – has to be considered.
Measurements may be ubiquitous, but tools for handling measurement uncertainty are harder to find.
The idea of an uncertain number was developed to address this problem and uncertain-number software has been written to provide much-needed support for processing measured data.
Uncertain numbers encapsulate information about the different contributions to the uncertainty of a result. They allow calculations involving measured quantities to be expressed like conventional-number calculations, while software can evaluate the measurement uncertainty automatically.
Several uncertain-number software tools have been developed and are available under licence for free.
The best of these is a programmable uncertainty calculator called the GUM Tree Calculator (GTC). GTC is a simple stand-alone application for Windows® that uses the Python programming language.
For more information see the latest version of the GTC documentation.
Other projects supporting uncertain numbers include: an add-in for Microsoft Excel® and a library for the R language.
The mathematics and statistics of uncertain numbers
Since 1993, the international measurement community has attempted to harmonise the evaluation and expression of measurement uncertainty by following recommendations in a document called The Guide to the Expression of Uncertainty in Measurement (GUM).
The uncertain-number approach follows these GUM guidelines. It also implements some extensions that apply to situations not covered in the GUM, such as the uncertainty of complex quantities.